1. Field of the Invention
The invention relates to a method and to an arrangement for checking a stability of an operating point of a circuit.
2. Description of the Related Art
A circuit, particularly an analog electrical circuit (analog circuit), frequently contains inherent instabilities (unstable operating points, unstable points), which are purposefully utilized for meeting given requirements. An example is a current comparator, which compares a reference current intensity with an input current intensity and sets an output voltage to one of two possible values depending on the difference between the two current intensities. Given this current comparator, there are two stable outside positions and one unstable middle position. The current comparator is based on the xe2x80x9cflip-flop principlexe2x80x9d.
It is generally of great interest to determine the stablity of individual operating points of the circuit. For this purpose, it is conventional to generate a system response to individual, local configurations and to evaluate it (see L. O. Chua et al.: xe2x80x9cComputer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniquesxe2x80x9d, Prentice Hall, 1975 (Chua)). Only a local view of the dynamics of the circuit is received, and an extremely intense calculation is required for an evaluation dependent on the time t.
A continuation method for determining a DC transfer curve for a circuit is known from U. Feldmann et al.: xe2x80x9cAlgorithms for Modern Circuit Simulationxe2x80x9d, AExc3x9c, Vol. 46 (1992, No. 4, Hirzel-Verlag Stuttgart, pages 274-285 (Feldmann).
On the basis of an eigenvalue method according to R. Neubert: xe2x80x9cAn Effective Method for the Stability Analysis of Steady States in the Simulation of Large Electrical Networksxe2x80x9d, In: W. Mathis and P. Noll (eds.), 2nd ITG discussion: Neue Anwendungen theoretischer Konzepte in der Elektrotechnik, pages 41-48, Berlin, (4) 1995, ITG, VDE-Verlag., a determination is made for an operating point of a circuit as to whether it is an asymptotically stable point (attractor) or an unstable point.
An object of the invention is to provide a method and an arrangement, which allows direct calculation of a global dynamic for a circuit.
This object is achieved by a method and an associated apparatus for determining a global dynamics of an electrical circuit, comprising the steps of determining a DC transfer curve of the circuit; performing a stability analysis for points of the DC transfer curve, the stability analysis determining for each point whether each point is an asymptotically stable point or an unstable point; determining a stable region of the DC transfer curve based on the asymptotically stable points; determining an unstable region of the DC transfer curve based on the unstable points; and outputting global dynamics of the circuit based on the stable region and the unstable region.
Further developments may include checking a stability of an operating point by the allocation of the operating point to the closest stable region of the DC transfer curve. The DC transfer curve may be determined by a continuation method, and/or the stability analysis may be carried out with an eigenvalue method. In the inventive method, the unstable region may have a process tolerance which is directly proportional to a sensitivity and indirectly proportional to a speed of the circuit, a variable group being defined by the process tolerance, the sensitivity, and the speed. The method may determine this sensitivity, speed, and process tolerance of the circuit. In the invention, the method may further comprise the steps of fixing at least one of the variables in the variable group; and dimensioning remaining unfixed variables in the variable group based on the fixed variables. This method may be used to design a comparator circuit (which may be a current comparator circuit) or a memory circuit. A functionality for designing circuits utilizing at least one instability may be provided by the method. The elements of the invention are explained in greater detail below.
For achieving this object, a method for determining a global dynamic of a circuit is proposed, in which a DC transfer curve of the circuit is determined. A stability analysis is carried out for points of the DC transfer curve that determines whether or not points of the DC transfer curve are asymptotically stable. Furthermore, at least one stable area of the DC transfer curve and at least one unstable area of the DC transfer curve are determined, where each area contains a series of coherent stable or unstable points. Therefore, the dynamics of the circuit is determined by at least one stable area and at least one unstable area. Coherent points are points of the same allocation xe2x80x9cstablexe2x80x9d or xe2x80x9cunstablexe2x80x9d.
On the basis of a successful determination of the (global) dynamics of the circuit, it is possible to determine a robustness of the circuit for individual points (also: operating points), which are not situated on the DC transfer curve. In an embodiment, an operating point is determined in that the operating point is allocated to the closest stable area of the DC transfer curve. In another embodiment, the DC transfer curve is determined by continuation methods (see Feldmann).
The DC transfer curve contains a stationary state or a plurality of stationary states dependent on a value occupancy of a parameter. For a dynamic system
G(,v,xcex)=0xe2x80x83xe2x80x83(1)
stationary solutions are determined in that the equation system
f(v, xcex):=G(0, v, xcex)=0(=0)xe2x80x83xe2x80x83(2)
is solved, where
 is a dynamic modification of a state vector,
v is a state vector and
xcex is a parameter.
Such an equation system (2) can be solved by standard methods, such as Newton method (see Chua).
The continuation method makes it possible to determine a next point on the DC transfer curve in that a next point is estimated in a direction along a probable curve of the DC transfer curve, and this point serves as initial value for the equation (2). Subsequent to a number of iterative steps, the correct next point results, which is actually situated on the DC transfer curve (at least within a prescribed approximation).
In the framework of the stability analysis, the points of the DC transfer curve are examined regarding their stability. On the basis of the eigenvalue method (see Neubert), in particular, asymptotic stability is checked preferably for each point or a fixed number of points on the DC transfer curve. Such a point is defined as an attractor. The attractor is determined in that all points run toward it concerning the stability within a small environment around it. The attractor therefore represents a stable center for its immediate environment.
A separation of the stable outside positions by the unstable middle position can result from the result of the stability analysis, particularly given comparator circuits.
Advantageously, the chronological dependencies of the circuit need not be considered with respect to the described determination of the global dynamics.
On the basis of a plurality of individual local output configurations, an integration (transient analysis) has previously been carried out. The result is interpreted by expert knowledge in order to be able to draw a conclusion regarding the sought global dynamics of the circuit. A time expenditure of up to 30 minutes can be expected for a transient analysis (for only one initial point), whereas it is possible to determine the global dynamics (without expert knowledge) by the method of the present invention in 10 minutes. Therefore, it is also possible to use the method as preprocessing step, which is potentially followed by a transient analysis for individual points, which are of particular interest.
In the framework of an additional embodiment, the unstable region can have a process tolerance (xcex94T), which is directly proportional to a sensitivity (xcex94s) and indirectly proportional to a speed of the circuit.
In an embodiment or design of an (electrical) circuit, it is advantageous to be able to represent all competing variables at once. Such competing variables are the speed of the circuit, the sensitivity and the process tolerance of the circuit (conditioned by the production). In a design phase of the circuit, specific values for specific target variables are determined for a default in respective cases. For example, the speed and the sensitivity of the circuit are competing targets; a compromise solution is determined between both.
In an embodiment of the invention, the described method is used for designing a comparator circuit, particularly a current comparator circuit. In another embodiment, the method is used for designing a memory circuit.
Generally, the described methods can be particularly utilized for designing circuits, in which at least one instability is used in order to obtain a functionality. Given the current comparator, the instability is used in order to control a high output value (preferably a voltage) with a low current.
For achieving the invention, an arrangement for checking a stability of an operating point of a circuit is also provided, which has a processor unit configured such that:
1) a DC transfer curve of the circuit can be determined;
2) a stability analysis can be carried out for points of the DC transfer curve, which determines whether or not each point is an asymptotically stable point;
3) a stable region of the DC transfer curve contains the asymptotically stable points and an unstable region of the DC transfer curve contains the unstable points;
4) the global dynamics of the circuit are characterized by the at least one stable region and the at least one unstable region.
This arrangement is particularly suitable for implementing the inventive method or one of its previously described further developments.